Depending on whether we require modular invariance under the full modular group or just an index two subgroup [1]}, [2]}, [3]}, an MDE is called respectively untwisted or twisted. The space of possible MDEs is labelled by a finite set of real parameters, the number of which depends only on the degree of the differential equation and whether it is untwisted or twisted. In this work we will focus mainly on untwisted MDEs, of which we will give some examples below.The twisted case is required if one allows for Schur operators with half-integer chiral dimension, and as such is the most general case. The untwisted case is a specialization of the twisted one (allowing for Schur operators of only integer dimension), and thus at a given order the untwisted case involves a smaller number of real parameters than the twisted one.
